Statistically Speaking, It's Probably a Good Game, Part 1: Probability for Game Designers

Quiz Time — Whoopee!

Q1)
You are designing a new MMORPG, and you set a particular item — Orc
Nostril Hair - to drop 10% of the time when a certain species of
monster is killed. One of your testers reports back that he killed 20
of the monsters, and found the Orc Nostril Hair 4 times. Another tester
killed 20 of the monsters and never found a single Orc Nostril Hair. Is
there a programming bug?

Orc Nostril Hair FollicleImage of Similar Hair Courtesy Wikipedia

Q2)
You are designing a combat system for a game and have decided to
include a critical hit mechanic. If the character lands a successful
hit (say 75% base chance to hit), then you roll another hit check. If
the second hit check is successful, the player will do double damage
(2x). However, if this happens, you roll another hit check, and if that’s
successful, then the damage is upgraded to triple damage (3x). As long
as each hit check is successful, you keep making new checks, and the
damage multiplier keeps increasing until a hit check is missed. What
percentage of the time will the player get at least double damage (2x)?
What percentage of the time will the player get quadruple damage (4x)
or better?

Q3) You have decided to include
a gambling mini-game in your latest magnum opus
RTS-FPS-tamagotchi-sports hybrid game. The gambling mini-game will be
very simple: the player can wager rubies on whether a coin flip will
come up heads or tails. The player always receives even money on his
winning bets. You will make the coin flip as fairly programmed as
possible (50%/50%), but you will include an extra feature for the
player: a list of the last 20 coin flip results will be shown on the
right side of the screen. Should you beg the programmers to include any
extra logic to prevent the player from taking advantage of this 20-flip
history and using it to bankrupt your entire in-game economy?

We’ll attack the answers to these captivating questions at the end of this piece (if you’re still awake).

Game Designers - Renaissance People and Anti-Experts

Designerus Gamus

Being
a designer in this day and age requires a pretty wide variety of
skills. Designers are the generalists of the development team, needing
to bridge the gap between Art and Engineering, competently
communicating with each — or at least competently faking it. A good
designer requires a basic understanding of a lot of different things,
because game design is a haphazard amalgamation of subjects.

It’s
pretty common to hear designers debating or waxing poetic on the finer
points of linear or non-linear storytelling, human psychology, control
ergonomics, or the integration of non-interactive sequences; less often
do you catch them mulling over the bare bones details of the hard
sciences like calculus, physics, or statistics. Sure, there are the
Will Wrights, determined to find fun in celestial goo and the dynamics
of city traffic planning. Most, though, wince when equations start
breathing down their necks.

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